If you are on a budget, I would suggest the i5 3570K and the EVGA GTX 670 FTW. The FTW card is even faster and beats the reference GTX 680 in most games and it's $100 cheaper. You can get the i7 3770K, but you will not see any improvements over the i5 in gaming.
For gaming a video card is usually more important, and a 3570 vs a 3770 in gaming is almost no difference. If you overclock them, they're basically on par in terms of gaming, that's why a better video card would all the difference. Gaming is rarely CPU limited, only when you have a total crap CPU paired with an awesome video card. Really the only difference between the 3570k and the 3770k is HT and slightly larger cache + 100mhz. HT doesn't do anything for gaming, and the cache rarely (but sometimes) has an effect. Therefore the GTX 680 is the better choice. But if I were you, I'd just OC my 670 and get a 3570 and save some money.